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% ****************** TITLE ****************************************

\title{Feedback}




\maketitle



\section{Reviewer 3}

Overall, the idea is nice and plausible. The presentation was also
good in general. However, there are several points where the authors
can improve on:
\begin{enumerate}
         \item In section 3.3, the distributions of the lengths and slopes of
the lines in a cluster are assumed to be 1-dimensional Gaussian
Distributions. However, this assumption has never been justified.
The authors should justify it through analysis or at least through
experiments.
         \textbf{Feedback}: In many real life applications, the system operates in different
states; and in each state, the system exhibits stable behavior. Each
observation of one state can be regarded as the stable behavior plus
some errors. Since the observational error in an experiment is often
described by Gaussian Distribution, we use it here to describe the
distribution of segment lines.
         \item In Algorithm 1, indexes for the loops seem not correct. For
example, in lines 2 and 5, the initial indexes should be 3 and 2
respectively. Also it seems that line 11 always evaluated false
because $\delta_t(i)$ is initialized to 1 in line 4. The algorithms
should be cleaned up.\\
         \textbf{Feedback}: The algorithm is modified as follows. The
         initialization of $\delta_1(i)$ is added in line 2. In line
         11-12, we add the initialization of $\delta_{t-d}(i)$ is
         the segment starts from the beginning of the time series.
%\label{app:algorithm}
\begin{algorithm}
\caption{Detect\_state\_sequence}\label{al:viterbi}
\begin{algorithmic}[1]
\State \textbf{Input} $\varepsilon_r$:maximal error threshold of
line approximation
 \State Initialize $\delta_1(i)=0$ ($1\leq i\leq K$)
 \For{$t\gets 2, n$}
    \For{$i\gets 1,K$}
        \State $\delta_t(i)=0$
        \For{$d\gets 2,t$}
            \State $L=BestLine(t-d+1,t)$
            \If{$Err(L)>\varepsilon_r$}
                \State Break
            \Else
                \If{$t==d$}
                    \State $temp=\pi_ib_i(L)$
                \Else
                    \State $temp=\max\limits_{j}(\delta_{t-d}(j)\cdot a_{ji})b_i(L)$
                \EndIf
                \If{$temp>\delta_t(i)$}
                    \State $\delta_t(i)=temp$
                    \State $prev_d(t)=t-d$
                    \State $prev_s(t)=j$
                \EndIf
            \EndIf
        \EndFor
    \EndFor
\EndFor \State Obtain maximal optimal probability $\delta_n(i)$,
which holds
\[\delta_n(i)\geq \delta_n(j),j\neq i\]
\State Obtain state sequence by backtracking sequence of $prev_s$
\State Obtain line sequence by backtracking sequence of $prev_d$
\end{algorithmic}
\end{algorithm}
         \item More importantly, it would have been nice if the evaluation included binary predication accuracy for predicting up or down instead of just giving relative error on the slopes. It would give more tangible idea about the performance because one can compare the accuracy with a natural baseline with the expected accuracy of 50\% (e.g., random, or always up; i.e., no learning cases). If the accuracy of the proposed model is better than 50% with meaningful margin, it may be significant in some domains like stock prediction.
         \item In page 9, right column, 3rd paragraph, line 1. $\epsilon_r$
should be $\epsilon_c$ 2) there is no explanation distinguishing
Minimal GC and Average GC in Table 2.\\
\textbf{Feedback}: We change $\epsilon_r$ to $\epsilon_c$ as
mentioned by the reviewer. We add the explanation distinguishing
Minimal $GC$ and Average $GC$ in Table 2 as follows: Then, for each
state of "French Franc", we compute its pattern-based
correlation($GC$) with any state in other 5 time series. Table 2
shows both minimal $GC$ and average $GC$. For example, in the first
row, Minimal $GC$ means the minimal $GC$ computed between any state
pair in which one is from "French Franc" and the other is from
"Australian Dollar". Average $GC$ is the average of all $GC$s
between all state pairs from these two currencies.
\end{enumerate}



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